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Yakk · 02-10-2005, 09:41 AM

m*a/(1-(v/c)^2)^.5 = -K/r^2

m/K * a * r^2 = -(1-(v/c)^2)^(1/2)

Let c = 1 by choice of units (ie, time seconds and distance in light-seconds -- always a good idea when working in relativity!)

r`` * r^2
---------------- = (-K)/m
(1-(r`^2))^(1/2)

This looks like a non-linear second order differential equation. I think you are fucked? My knowledge of this area of math is very sparse.

By 'fucked' I mean I don't know of any non-numeric means of modelling this. Numeric models exist, of course, but they look more like computer programs than equations.

I'm wondering -- wouldn't there be time and space dialations/contractions as well, which are missing from your equation? This could either simplify or complicate the situation. I'd have to hit up my relativity-knowing friend.

Second, initial conditions will matter. It wouldn't be that hard to solve the position/accelleration/velocity if the two objects where moving in a perfect orbit around each other, or so I'd guess...

I also wonder if conservation of mass/energy might be of help here... From your perspective, as you see someone falling towards you, they are losing potential 'gravitic' energy and gaining kinetic energy. Isn't this a net zero change in their energy, and hence a net zero change in their mass?

02-10-2005, 09:41 AM	#9 (permalink)
Yakk Wehret Den Anfängen! Location: Ontario, Canada	ma/(1-(v/c)^2)^.5 = -K/r^2 m/K a * r^2 = -(1-(v/c)^2)^(1/2) Let c = 1 by choice of units (ie, time seconds and distance in light-seconds -- always a good idea when working in relativity!) r`` * r^2 ---------------- = (-K)/m (1-(r`^2))^(1/2) This looks like a non-linear second order differential equation. I think you are fucked? My knowledge of this area of math is very sparse. By 'fucked' I mean I don't know of any non-numeric means of modelling this. Numeric models exist, of course, but they look more like computer programs than equations. I'm wondering -- wouldn't there be time and space dialations/contractions as well, which are missing from your equation? This could either simplify or complicate the situation. I'd have to hit up my relativity-knowing friend. Second, initial conditions will matter. It wouldn't be that hard to solve the position/accelleration/velocity if the two objects where moving in a perfect orbit around each other, or so I'd guess... I also wonder if conservation of mass/energy might be of help here... From your perspective, as you see someone falling towards you, they are losing potential 'gravitic' energy and gaining kinetic energy. Isn't this a net zero change in their energy, and hence a net zero change in their mass? __________________ Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.